SOLVE COMPOUND INEQUALITIES2x<8 and 4x+4>-8

Question

2x<8 and 4x+4>8

Answer 1

Tan

 

The first inequality can be solved as follows:

 

2x<8

Divide both sides by 2 to get x<4.

 

 

The second inequality can be solved as follows:

 

4x+4>8

Subtract 4 from both sides:          4x>8-4

                                                 4x>4

Now divide both sides by 4:          x>1

 

So the answer is x<4 and x>1  or   1<x<4

 

Hope this helps!

 

George T

Answer 2

Start with the second half.  Solve 4x+4>8.  For simplicity think of > as an =.  Divide both sides by 4.  4x/4+4/4=8/4 equals x+1=2.  Subtract 1 from both sides.  (x+1)-1=2-1 equals x=1.   Since the formula is using > instead = we used to make it easier to understand, x>1.  Therefore x can be any number larger than 1.  This is the lower boundary for our Compound Inequality.  

 

Now try it with the second formula.  2x<8.   Solve for x assuming < is an = for simplicity.  2x=8.  Divide both sides by 2 to solve for x.  2x/2 =8/2.  equals x=4. 

 

Now we have both boundaries for x      1 < x < 4